Abstract
Thermal design with nanoscale is essential when developing miniaturized electronic devices. Whereas conventional macroscale thermal design methods have a limitation to improve the performance of an electronic device, the implementation of nanostructural designs that utilizes unique properties of heat conduction has resulted in unprecedentedly high-performance electronic devices. One of the most unique and useful properties in a nanoscale heat conduction is a temperature discontinuity on a material surface. However, few reports proposed thermal-design criteria and thermal designs have been dependent on heuristic approaches. There is a large demand for constructing the design guidelines of nanoscale thermal problems and one of the effective design criteria is a shape sensitivity which indicates how to set the material surfaces based on physics and mathematics. In this paper, we propose a shape sensitivity analysis method for a two-phase thermal design problem considering temperature discontinuities. First, we clarify the design problem of a nanoscale heat conduction based on the Boltzmann transport equation. Next, we construct a method for a shape sensitivity analysis for a heat conduction problem considering two-phase nanoscale effects by expanding the work of Pantz. The validity of our shape sensitivity analysis is demonstrated through a numerical example.
